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Four friends Laura, Nancy, James and Simon buy some pencils,

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Four friends Laura, Nancy, James and Simon buy some pencils, [#permalink]

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New post 19 Aug 2013, 20:13
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Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?


Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

OA:
[Reveal] Spoiler:
$9.5

Last edited by Bunuel on 20 Aug 2013, 02:07, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Simultaneous equations [#permalink]

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New post 20 Aug 2013, 01:14
vinayparamanand wrote:
Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?


Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

A: $9.5


Let the cost of a pencil be $x
Let the cost of a pen be $y
Let the cost of a erasers be $z

Now,
for Laura 5x+6y+z = 17.50 ----a
for Nancy 3x+3y+2z=10 ----b
for James 2x+5y+5z=14.50 ---c

We have to find value for Simon i.e 3x+2y+5z=??

Now,
2b - a => x + 3z = 2.5 ----d
5b - 3c => 9x - 5z = 6.5 ------e

Solving, d and e

9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5
32z = 16
z = 1/2

putting z in d, we get x = 1
putting z and x in a we get y= 2

3x + 2y +5z = 3 + 4 + 2.5 => 9.5$

Thanks,
Jai

KUDOS if it HELPED..!!! :)
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MODULUS Concept ---> http://gmatclub.com/forum/inequalities-158054.html#p1257636
HEXAGON Theory ---> http://gmatclub.com/forum/hexagon-theory-tips-to-solve-any-heaxgon-question-158189.html#p1258308

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Re: Simultaneous equations [#permalink]

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New post 01 Sep 2013, 11:56
I agree with the solution provided here, but I would like to know an alternative way that is easier and can be done in the shortest amount of time possible. The current approach is lengthy and time-consuming.
Thanks.
jaituteja wrote:
vinayparamanand wrote:
Four friends Laura, Nancy, James and Simon buy some pencils, pens and erasers from a shop. Laura buys 5 pencils, 6 pens, and 1 eraser for $17.50. Nancy buts 3 pens, 3 pencils, and 2 erasers for $ 10. James buys 5 pens, 2 pencils, and 5 erasers for $14.50. How much will Simon have to pay if he buys 3 pens, 2 pencils, and 5 erasers?


Note: How often in the GMAT do such questions appear?
Can i have a generic way to solve such questions?

A: $9.5


Let the cost of a pencil be $x
Let the cost of a pen be $y
Let the cost of a erasers be $z

Now,
for Laura 5x+6y+z = 17.50 ----a
for Nancy 3x+3y+2z=10 ----b
for James 2x+5y+5z=14.50 ---c

We have to find value for Simon i.e 3x+2y+5z=??

Now,
2b - a => x + 3z = 2.5 ----d
5b - 3c => 9x - 5z = 6.5 ------e

Solving, d and e

9d - e => 9x + 27z - (9x-5z ) = 22.5 - 6.5
32z = 16
z = 1/2

putting z in d, we get x = 1
putting z and x in a we get y= 2

3x + 2y +5z = 3 + 4 + 2.5 => 9.5$

Thanks,
Jai

KUDOS if it HELPED..!!! :)

Kudos [?]: 10 [0], given: 1

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Re: Four friends Laura, Nancy, James and Simon buy some pencils, [#permalink]

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New post 26 Sep 2017, 04:24
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Re: Four friends Laura, Nancy, James and Simon buy some pencils,   [#permalink] 26 Sep 2017, 04:24
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